Some Fixed Point Theorems In Cone Metric Spaces With Banach Algebras

The fixed point theory in one metric space is an important part of nonlinear functional analysis. Since Hao Liu and Shaoyuan Xu recently introduced the concept of cone metric space with Banach algebra, replacing Banach space by Banach algebra, Fixed point theory on this space has become many scholars Hot topic of research in recent years to give some very important results, In this paper, we generalize some classical fixed point theorems in the cone metric space by using the iteration method, Some new fixed point theorems in cone metric space with the Banach algebra arc obtained. The results are as follows:1. Proposed the concept of cone metric space with the Banach algebra, proved that in cone metric space with the Banach algebra some fixed point theorems of partially ordered set2. The c-distance are defined in the cone metric space with the Banach algebra, and studied some of its basic properties, based on this the fixed point theorem of the c-distance in the metric space with the Banach algebra is proved.3. The definition of expansion mapping and its related properties are given. The fixed point theorems for the extension of the cone metric space with the Banach algebra are studied.